Viscosity and Mean Free Path of Very Diluted Solutions of 3He in 4He

Abstract

We have measured the laminar friction of various diluted ³He-⁴He mixtures, of natural ⁴He and of isotopically pure ⁴He on an oscillating sphere below 1 K. For ³He concentrations x ₃ ranging from 10 ⁻² to 10 ⁻⁴ we find a reduction of the drag above 0.5 K when compared to the pure liquid and a large enhancement below, which is almost independent of x ₃ . At low concentrations 5·10 ⁻⁵>x ₃ ≥5·10 ⁻⁷ the drag becomes proportional to x ₃ which implies a transition from a hydrodynamic to a ballistic regime. This is confirmed by deducing the mean free path of the ³He atoms from the data. The temperature dependence of the drag in the ballistic regime, however, is found to be proportional to T and therefore different from the expected T^1/2 behaviour.